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Let $d\\geq 2$ be a natural number and $\\boldsymbol{\\alpha}=(\\alpha_d,\\ldots, \\alpha_1)\\in \\mathbb{R}^d.$ Define the exponential sum \\begin{equation*}\n  f_d(\\boldsymbol{\\alpha};N):=\\sum_{1 \\leq n \\leq N}e(\\alpha_d n^d + \\cdots+ \\alpha_1 n). \\end{equation*} For $p>0$, consider mean values of the exponential sums \\begin{equation*}\n  \\mathcal{I}_{p,d"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2506.01751","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NT","submitted_at":"2025-06-02T14:59:11Z","cross_cats_sorted":[],"title_canon_sha256":"c41b3959847955dcd5d5893ebad0a712cd1532c656379ced874c65249b0d301b","abstract_canon_sha256":"8ce7773e32424db07d5ca8dc2867645d11abac56144218c915503c0cf240fa60"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:26:31.764235Z","signature_b64":"JQEec7p5ysn2ylBeztEdXl0yGLpjCXgxgLhBc6D3KPpQy+rJOnriU+256wreDh3XCNcbdZ0mRYMZGtBPhPUiCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1290d7e9ca454daccae2ff96593e805e87673f37c21b8a00d467f1c3e491b1fe","last_reissued_at":"2026-07-05T11:26:31.763782Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:26:31.763782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An extended Vinogradov's mean value theorem","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Changkeun Oh, Kiseok Yeon","submitted_at":"2025-06-02T14:59:11Z","abstract_excerpt":"In this paper, we provide novel mean value estimates for exponential sums related to the extended main conjecture of Vinogradov's mean value theorem, by developing the Hardy-Littlewood circle method together with a refined shifting variables argument. Let $d\\geq 2$ be a natural number and $\\boldsymbol{\\alpha}=(\\alpha_d,\\ldots, \\alpha_1)\\in \\mathbb{R}^d.$ Define the exponential sum \\begin{equation*}\n  f_d(\\boldsymbol{\\alpha};N):=\\sum_{1 \\leq n \\leq N}e(\\alpha_d n^d + \\cdots+ \\alpha_1 n). \\end{equation*} For $p>0$, consider mean values of the exponential sums \\begin{equation*}\n  \\mathcal{I}_{p,d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.01751","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.01751/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2506.01751","created_at":"2026-07-05T11:26:31.763840+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.01751v2","created_at":"2026-07-05T11:26:31.763840+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.01751","created_at":"2026-07-05T11:26:31.763840+00:00"},{"alias_kind":"pith_short_12","alias_value":"CKINP2OKIVG2","created_at":"2026-07-05T11:26:31.763840+00:00"},{"alias_kind":"pith_short_16","alias_value":"CKINP2OKIVG2ZSXC","created_at":"2026-07-05T11:26:31.763840+00:00"},{"alias_kind":"pith_short_8","alias_value":"CKINP2OK","created_at":"2026-07-05T11:26:31.763840+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.04948","citing_title":"An Integral Mean Value Theorem for Weyl Sums over Broken Arcs","ref_index":11,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CKINP2OKIVG2ZSXC76LFSPUAL2","json":"https://pith.science/pith/CKINP2OKIVG2ZSXC76LFSPUAL2.json","graph_json":"https://pith.science/api/pith-number/CKINP2OKIVG2ZSXC76LFSPUAL2/graph.json","events_json":"https://pith.science/api/pith-number/CKINP2OKIVG2ZSXC76LFSPUAL2/events.json","paper":"https://pith.science/paper/CKINP2OK"},"agent_actions":{"view_html":"https://pith.science/pith/CKINP2OKIVG2ZSXC76LFSPUAL2","download_json":"https://pith.science/pith/CKINP2OKIVG2ZSXC76LFSPUAL2.json","view_paper":"https://pith.science/paper/CKINP2OK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.01751&json=true","fetch_graph":"https://pith.science/api/pith-number/CKINP2OKIVG2ZSXC76LFSPUAL2/graph.json","fetch_events":"https://pith.science/api/pith-number/CKINP2OKIVG2ZSXC76LFSPUAL2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CKINP2OKIVG2ZSXC76LFSPUAL2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CKINP2OKIVG2ZSXC76LFSPUAL2/action/storage_attestation","attest_author":"https://pith.science/pith/CKINP2OKIVG2ZSXC76LFSPUAL2/action/author_attestation","sign_citation":"https://pith.science/pith/CKINP2OKIVG2ZSXC76LFSPUAL2/action/citation_signature","submit_replication":"https://pith.science/pith/CKINP2OKIVG2ZSXC76LFSPUAL2/action/replication_record"}},"created_at":"2026-07-05T11:26:31.763840+00:00","updated_at":"2026-07-05T11:26:31.763840+00:00"}